Joint seismic and petrophysical nonlinear inversion with Gaussian mixture-based adaptive regularization

Abstract

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating the petrophysical properties of rocks to observed seismic data is highly nonlinear, and solving the relevant inverse problem is a challenging task. We have developed a novel inversion method for jointly estimating the elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we have developed a regularization term based on the prior Gaussian mixture model under a Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared with sequential inversion and nonadaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.